ArticleAnnals of the New York Academy of Sciences2022
Measurement of the neutral axis in avian eggshells reveals which species conform to the golden ratio.
Article in Annals of the New York Academy of Sciences, 2022. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 9 papers.
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9 citing papers in PubMed, 17 citations in OpenAlex.
- Genome-Wide Egg Hunt: Unhiding Candidate Genes for Egg Component Traits in Layers of an FAnimals : an open access journal from MDPI · 2025Article
- Pear-Shaped Eggs Evolved to Maximize the Surface Area-to-Volume Ratio, Increase Metabolism, and Shorten Incubation Time in Birds.Integrative zoology · 2025Article
- Smart and smarter: improving on a classic egg shape model.Theory in biosciences = Theorie in den Biowissenschaften · 2025Article
- Coupling Artificial Intelligence with Proper Mathematical Algorithms to Gain Deeper Insights into the Biology of Birds' Eggs.Animals : an open access journal from MDPI · 2025Article
- Accurate calculation of the content volume, density and original weight of museum curated eggs.Scientific reports · 2024Article
- Extending Genetic Algorithms with Biological Life-Cycle Dynamics.Biomimetics (Basel, Switzerland) · 2024Article
- A novel model for eggs like pears: How to quantify them geometrically with a mathematical formula of two parameters?Journal of biosciences · 2023Article
- Measurement of the neutral axis in avian eggshells reveals which species conform to the golden ratio.Annals of the New York Academy of Sciences · 2022Article
- Egg-inspired engineering in the design of thin-walled shelled vessels: a theoretical approach for shell strength.Frontiers in bioengineering and biotechnology · 2022Article
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4 authors at 3 institutions in 2 countries.
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No grant is acknowledged in the PubMed record.
Abstract
Avian eggs represent a striking evolutionary adaptation for which shell thickness is crucial. An understudied eggshell property includes the neutral axis, a line that is drawn through any bent structure and whose precise location is characterized by the k-factor. Previous studies have established that, for chicken eggs, mean k corresponds to the golden ratio (Φ = 1.618, or 0.618 in its reciprocal form). We hypothesized whether such an arrangement of the neutral axis conforms to the eggshell of any bird or only to eggshells with a certain set of geometric parameters. Implementing a suite of innovative methodological approaches, we investigated variations in k of 435 avian species, exploring which correspond to Φ. We found that mean k is highly variable among birds and does not always conform to Φ, being much lower in spherical and ellipsoid eggs and higher in pyriform eggs. While 21 species had k values within 0.618 ± 0.02 (including four falcon species) and the Falconinae subfamily (six species) revealed a mean of 0.618, it is predominantly domesticated species (chicken, ducks, and geese) that lay eggs whose neutral axis corresponds to the golden ratio. Thus, the study of the mathematical secrets of the eggshell related to the golden ratio of its neutral axis suggests its species-specific signatures in birds.
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